Question: $B$ is the midpoint of $\overline{AC}$ $A$ $B$ $C$ If: $ AB = 8x + 4$ and $ BC = 3x + 19$ Find $AC$.
A midpoint divides a segment into two segments with equal lengths. ${AB} = {BC}$ Substitute in the expressions that were given for each length: $ {8x + 4} = {3x + 19}$ Solve for $x$ $ 5x = 15$ $ x = 3$ Substitute $3$ for $x$ in the expressions that were given for $AB$ and $BC$ $ AB = 8({3}) + 4$ $ BC = 3({3}) + 19$ $ AB = 24 + 4$ $ BC = 9 + 19$ $ AB = 28$ $ BC = 28$ To find the length $AC$ , add the lengths ${AB}$ and ${BC}$ $ AC = {AB} + {BC}$ $ AC = {28} + {28}$ $ AC = 56$